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Good Afternoon!

Good Afternoon!. Today we will be learning about Multiplying 2 decimal places by whole numbers. Let’s warm up :. Solve:. 1) 822. 1) 274 x 3. 2) 381,163. 2) 5,689 x 67. 3) 349,370. 3) 3,565 x 98. Estimate:. 4) 8,567 x 93. 4) 774,000. 5) 596 x 12. 5) 6,000.

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Good Afternoon!

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  1. Good Afternoon! Today we will be learning about Multiplying 2 decimal places by whole numbers Let’s warm up : Solve: 1) 822 1) 274 x 3 2) 381,163 2) 5,689 x 67 3) 349,370 3) 3,565 x 98 Estimate: 4) 8,567 x 93 4) 774,000 5) 596 x 12 5) 6,000 CONFIDENTIAL

  2. Let’s first review what we learnt about Multiplication in the previous sessions before proceeding further. We discussed about the following terms. Product 4 x 5 = 20 Factor Factor: Number that is multiplied to give a product. Product: Number that is obtained by multiplying numbers. • Multiple: It is the product of a number and any whole number. 4 and 6 are both multiples of 2. • Even numbers: Whole numbers that are divisible by 2 are even numbers. Like the numbers 2, 4, 6, 8 and 10. These numbers are the multiples of 2. • Odd numbers: Whole numbers that are not divisible by 2 are odd numbers. Like the numbers 1, 3, 5, 7, and 9. These numbers are not the multiples of 2. CONFIDENTIAL

  3. Review There are several properties of Multiplication. 1) COMMUTATIVE PROPERTY: We can change the order of the factors and the product stays the same. EXAMPLE: 4 x 3 = 12 3 x 4 = 12 2) IDENTITY PROPERTY: We can multiply a number by 1and the product is the number. EXAMPLE: 3 x 1 = 3 3) ZERO PROPERTY: We can multiply a number by 0 and the product is zero. EXAMPLE: 7 x 0 = 0 CONFIDENTIAL

  4. Review Find: 236 x 6 We multiply numbers by first lining up the digits in the following manner: STEP 1: Regroup 36 as 3 tens and 6 ones. First multiply 6 with 6 to obtain 36. 3 236 X 6 6 STEP 2: Again, multiply 6 with 3 at the tens place to obtain 18. Then, add 3 and 18 to obtain 21. Regroup 21 as 2 hundreds and 1 tens. 23 236 X 6 16 CONFIDENTIAL

  5. Review Then, multiply 6 with 2 at the hundreds place to obtain 12. Then, 2 and 12 to obtain 14. STEP 3: Hence, the result. 23 236 X 6 1416 • By Estimate, we mean an answer that is close to the exact answer. Estimate 6 x 44. While estimating products, we round the greater factor. 6 x 44. Round to the nearest tens. 6 x 40 =240 CONFIDENTIAL

  6. Review We can make a multiplication table by skip counting on the number line. 5 5 5 5 5 5 5 5 5 5 0 5 10 15 20 25 30 35 40 45 50 The multiplication table of 5 would be like this: RULE:5 x n , where ‘n’ is any whole number CONFIDENTIAL

  7. Review DECIMAL: A number that uses place value and a decimal point to show tenths, hundredths and the thousandths. • 0.1 is a decimal number for one tenth. • 0.12 is a decimal number for twelve hundredths. • 0.125 is a decimal number for one hundred twenty-five thousandths. DECIMAL POINT: A period separating the ones and the tenths in the decimal is the Decimal Point. CONFIDENTIAL

  8. Let’s start with Multiplying 2 decimal places by whole numbers How many decimal places are in the given Decimal Numbers? • Count the number of digits after the decimal. This gives the decimal place in the given number. There are two decimal places in the decimal number. 1.75 There are three decimal places in the decimal number. 1.387 There is one decimal place in the decimal number. 2.8 CONFIDENTIAL

  9. You are familiar with multiplication of whole numbers. Now we will consider the multiplication of a decimal by a whole number . Multiplying decimals is very similar to multiplying whole numbers. The only extra step is to decide how many digits to leave to the right of the decimal point. To do that, add the numbers of digits to the right of the decimal point in both factors. CONFIDENTIAL

  10. Multiplication is repeated addition. So, 1.5 x 2 = 1.5 + 1.5 = 3.0 This can be represented on the number line as follows: 2 1 0 3 4 + 1.5 1.5 Here, we see that there is one decimal place in the number being multiplied. 1.5 x 2 There is one decimal place in the answer. 3.0 CONFIDENTIAL

  11. So, we see that, to multiply a decimal number by a whole number: • Ignore the decimal point and multiply the digits. • Place the decimal point in the answer so that it has the same number of decimal places as the number being multiplied. CONFIDENTIAL

  12. Multiply: 12.72 × 49 STEP 1: 12.72 Line up the numbers on the right--do not align the decimal points. ×  49 STEP 2: 12.72 Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers. ×  49 11448 5088 CONFIDENTIAL

  13. 12.72 STEP 3: ×  49 11448 Add the products. 5088 62328 STEP 4: 12.72 • Mark off decimal places equal to the number of decimal places in the numbers being multiplied. ×  49 11448 5088 623.28 CONFIDENTIAL

  14. Calculate 46.4 × 15. 46.4 1 decimal place in the number being multiplied. × 1 5 232 0 {Ignore decimal point for interim calculation.} + 464 1 decimal place in the answer. 696.0 Hence,46.4 × 15 = 696 • There is one decimal place in the decimal number being multiplied.  So, we place the decimal point one place from the right-hand end of the answer. • Any trailing zeros in the decimal places of the answer can be omitted. Calculate 977.5 × 22. 21504 CONFIDENTIAL

  15. BREAK CONFIDENTIAL

  16. GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/03-27-07-catnmouse.html CONFIDENTIAL

  17. Assignments How many decimal places are in the given Decimal Numbers? 1) 97.76 1) 2 2) 723.578 2) 3 3) 1 3) 234.3 4) 8.3457 4) 4 CONFIDENTIAL

  18. Multiply: 5) 97.76  x 4 5) 391.04 6) 723.5  x 34 6) 24,599 7) 4.76  x 93 7) 442.68 8) 7891.71 8) 33.87  x 233 9) 378. 24 x 25 9) 9456 CONFIDENTIAL

  19. 10) The cost of one pen is $1.65. Find the cost of 28 pens. 10) $ 46.2 CONFIDENTIAL

  20. Very Good! Let's Review We learnt to find the decimal places. How many decimal places are in the given Decimal Numbers? • Count the number of digits after the decimal. This gives the decimal place in the given number. There are two decimal places in the decimal number. 1.75 There are three decimal places in the decimal number. 1.387 There is one decimal place in the decimal number. 2.8 CONFIDENTIAL

  21. This can be represented on the number line as follows: 2 1 0 3 4 + 1.5 1.5 Here, we see that there is one decimal place in the number being multiplied. 1.5 x 2 There is one decimal place in the answer. 3.0 So, we see that, to multiply a decimal number by a whole number: • Ignore the decimal point and multiply the digits. • Place the decimal point in the answer so that it has the same number of decimal places as the number being multiplied. CONFIDENTIAL

  22. Multiply: 12.72 × 49 STEP 1: 12.72 Line up the numbers on the right--do not align the decimal points. ×  49 STEP 2: 12.72 Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers. ×  49 11448 5088 CONFIDENTIAL

  23. 12.72 STEP 3: ×  49 11448 Add the products. 5088 62328 STEP 4: 12.72 • Mark off decimal places equal to the number of decimal places in the numbers being multiplied. ×  49 11448 5088 623.28 CONFIDENTIAL

  24. Calculate 46.4 × 15. 46.4 1 decimal place in the number being multiplied. × 1 5 232 0 {Ignore decimal point for interim calculation.} + 464 1 decimal place in the answer. 696.0 Hence,46.4 × 15 = 696 • There is one decimal place in the decimal number being multiplied.  So, we place the decimal point one place from the right-hand end of the answer. • Any trailing zeros in the decimal places of the answer can be omitted. CONFIDENTIAL

  25. You have done a nice job. See you in the next session. CONFIDENTIAL

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